Green's Functions in Laplace Equations

Related lectures (31)

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Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores Green's Theorem, rotations, closed paths, and integral signs.

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Covers the theory and applications of Green's function in solving differential equations.

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.